A Physically Consistent Path-Weighted Diffusivity Function for Modeling of Drop-by-Drop Liquid Metal Deposition

A physically consistent path-weighted diffusivity function is derived for parametric representation of heat diffusion patterns occurring within a volume of material where in there exists inhomogeneous or anisotropic thermal diffusivity. A physically consistent parametric representation of energy deposition processes, where there exists spatially dependent thermal diffusivity, provides for more optimal inverse analysis of such processes. The path-weighted diffusivity function presented here further extends an inverse analysis approach presented previously. The general functional characteristics of the path-weighted diffusivity function derived are examined via a prototype simulation of drop-by-drop liquid metal deposition upon a material characterized by anisotropic thermal diffusivity. The results of this simulation are compared with previous simulations concerning path-weighted thermal diffusivity. The parametric representations presented, which are constructed using path-weighted sums of analytic basis functions, are examined from the perspective of discrete numerical methods. This perspective provides a foundation for the development of control algorithms for process optimization with respect to achieving specific microstructures within a fabricated structure.